The W sup (2) sub 3 conformal algebra and the Boussinesq hierarchy

Journal Article · Fri Aug 30 04:00:00 EDT 1991 · Modern Physics Letters A; (United States)

DOI:https://doi.org/10.1142/S0217732391002827· OSTI ID:5440342

Mathieu, P ^[1]; Oevel, W ^[2]

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1. Laval Univ., Quebec City, PQ (Canada). Dept. de Physique
2. Dept. of Mathematical Sciences, Univ. of Technology, Loughborough LE11 STU (GB)

In this paper the classical W{sub 3}{sup (2)} algebra of Polyakov is shown to be equivalent to the second Poisson structure of a new integrable hierarchy of nonlinear equations. This hierarchy is related to the Boussinesq hierarchy by interchanging the roles of the space and time variables x and t in the Boussinesq equation. From this relation the Miura map, relating the new hierarchy to its modified version, can be derived systematically. It is found to be equivalent to the known free field representation of the W{sub 3}{sup (2)} algebra.

• OSTI ID: 5440342
• Journal Information: Modern Physics Letters A; (United States), Journal Name: Modern Physics Letters A; (United States) Vol. 6:26; ISSN 0217-7323; ISSN MPLAE
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLASSICAL MECHANICS
CONFORMAL GROUPS
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
LIE GROUPS
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NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
SYMMETRY GROUPS